Abstract: Several studies have proposed that the shape of the Universe may be a
Poincare dodecahedral space (PDS) rather than an infinite, simply connected,
flat space. Both models assume a close to flat FLRW metric of about 30% matter
density. We study two predictions of the PDS model. (i) For the correct model,
the spatial two-point cross-correlation function, $\ximc$, of temperature
fluctuations in the covering space, where the two points in any pair are on
different copies of the surface of last scattering (SLS), should be of a
similar order of magnitude to the auto-correlation function, $\xisc$, on a
single copy of the SLS. (ii) The optimal orientation and identified circle
radius for a "generalised" PDS model of arbitrary twist $\phi$, found by
maximising $\ximc$ relative to $\xisc$ in the WMAP maps, should yield $\phi \in
\{\pm 36\deg\}$. We optimise the cross-correlation at scales < 4.0 h^-1 Gpc
using a Markov chain Monte Carlo (MCMC) method over orientation, circle size
and $\phi$. Both predictions were satisfied: (i) an optimal "generalised" PDS
solution was found, with a strong cross-correlation between points which would
be distant and only weakly correlated according to the simply connected
hypothesis, for two different foreground-reduced versions of the WMAP 3-year
all-sky map, both with and without the kp2 Galaxy mask: the face centres are
$(l,b)_{i=1,6}\approx (184d, 62d), (305d, 44d), (46d, 49d), (117d, 20d), (176d,
-4d), (240d, 13d) to within ~2d, and their antipodes; (ii) this solution has
twist \phi= (+39 \pm 2.5)d, in agreement with the PDS model. The chance of this
occurring in the simply connected model, assuming a uniform distribution $\phi
\in [0,2\pi]$, is about 6-9%.